Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

The generalized recurrent set, explosions and Lyapunov functions

Abstract : We consider explosions in the generalized recurrent set for homeomorphisms on a compact metric space. We provide multiple examples to show that such explosions can occur, in contrast to the case for the chain recurrent set. We give sufficient conditions to avoid explosions and discuss their necessity. Moreover, we explain the relations between explosions and cycles for the generalized recurrent set. In particular, for a compact topological manifold with dimension greater or equal 2, we characterize explosion phenomena in terms of existence of cycles. We apply our results to give sufficient conditions for stability, under C 0 perturbations, of the property of admitting a continuous Lyapunov function which is not a first integral.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [30 references]  Display  Hide  Download
Contributor : Anna Florio Connect in order to contact the contributor
Submitted on : Friday, April 12, 2019 - 10:55:35 AM
Last modification on : Tuesday, February 22, 2022 - 11:36:04 AM


Files produced by the author(s)


  • HAL Id : hal-02097706, version 1



Olga Bernardi, Anna Florio, Jim Wiseman. The generalized recurrent set, explosions and Lyapunov functions. 2019. ⟨hal-02097706⟩



Record views


Files downloads